




"""simple docstring"""





def        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      str:


			"""simple docstring"""
			if a < 0 or b < 0:
						raise ValueError("the value of both inputs must be positive"				)

			__UpperCAmelCase						:			Optional[Any]												=       str(bin(UpperCamelCase				)				)[2:]  # remove the leading "0b"
			__UpperCAmelCase						:			int												=       str(bin(UpperCamelCase				)				)[2:]  # remove the leading "0b"

			__UpperCAmelCase						:			Tuple												=       max(len(UpperCamelCase				)					,							len(UpperCamelCase				)				)

			return "0b" + "".join(
			    str(int(char_a != char_b				)				)
			    for char_a, char_b in zip(a_binary.zfill(UpperCamelCase				)					,							b_binary.zfill(UpperCamelCase				)				)				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()



"""simple docstring"""


from __future__ import annotations

import math





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   list:




						'''simple docstring'''



						if len(__lowerCAmelCase							) != 2 or len(a[0]							) != 2 or len(__lowerCAmelCase							) != 2 or len(b[0]							) != 2:
												raise Exception("Matrices are not 2x2"							)
						lowerCamelCase__   =[
						    [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
						    [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
						]
						return new_matrix





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Dict:




						'''simple docstring'''



						return [
						    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]							)							)]
						    for row in range(len(__lowerCAmelCase							)							)
						]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						return [
						    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]							)							)]
						    for row in range(len(__lowerCAmelCase							)							)
						]





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   tuple[list, list, list, list]:




						'''simple docstring'''



						if len(__lowerCAmelCase							) % 2 != 0 or len(a[0]							) % 2 != 0:
												raise Exception("Odd matrices are not supported!"							)

						lowerCamelCase__   =len(__lowerCAmelCase							)
						lowerCamelCase__   =matrix_length // 2

						lowerCamelCase__   =[[a[i][j] for j in range(__lowerCAmelCase  ,       __lowerCAmelCase							)] for i in range(__lowerCAmelCase							)]
						lowerCamelCase__   =[
						    [a[i][j] for j in range(__lowerCAmelCase  ,       __lowerCAmelCase							)] for i in range(__lowerCAmelCase  ,       __lowerCAmelCase							)
						]

						lowerCamelCase__   =[[a[i][j] for j in range(__lowerCAmelCase							)] for i in range(__lowerCAmelCase							)]
						lowerCamelCase__   =[[a[i][j] for j in range(__lowerCAmelCase							)] for i in range(__lowerCAmelCase  ,       __lowerCAmelCase							)]

						return top_left, top_right, bot_left, bot_right





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   tuple[int, int]:




						'''simple docstring'''



						return len(__lowerCAmelCase							), len(matrix[0]							)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   None:




						'''simple docstring'''



						print("\n".join(str(__lowerCAmelCase							) for line in matrix							)							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   list:




						'''simple docstring'''



						if matrix_dimensions(__lowerCAmelCase							) == (2, 2):
												return default_matrix_multiplication(__lowerCAmelCase  ,       __lowerCAmelCase							)

						lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =split_matrix(__lowerCAmelCase							)
						lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =split_matrix(__lowerCAmelCase							)

						lowerCamelCase__   =actual_strassen(__lowerCAmelCase  ,       matrix_subtraction(__lowerCAmelCase  ,       __lowerCAmelCase							)							)
						lowerCamelCase__   =actual_strassen(matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)  ,       __lowerCAmelCase							)
						lowerCamelCase__   =actual_strassen(matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)  ,       __lowerCAmelCase							)
						lowerCamelCase__   =actual_strassen(__lowerCAmelCase  ,       matrix_subtraction(__lowerCAmelCase  ,       __lowerCAmelCase							)							)
						lowerCamelCase__   =actual_strassen(matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)  ,       matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)							)
						lowerCamelCase__   =actual_strassen(matrix_subtraction(__lowerCAmelCase  ,       __lowerCAmelCase							)  ,       matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)							)
						lowerCamelCase__   =actual_strassen(matrix_subtraction(__lowerCAmelCase  ,       __lowerCAmelCase							)  ,       matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)							)

						lowerCamelCase__   =matrix_addition(matrix_subtraction(matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)  ,       __lowerCAmelCase							)  ,       __lowerCAmelCase							)
						lowerCamelCase__   =matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =matrix_subtraction(matrix_subtraction(matrix_addition(__lowerCAmelCase  ,       __lowerCAmelCase							)  ,       __lowerCAmelCase							)  ,       __lowerCAmelCase							)

						# construct the new matrix from our 4 quadrants
						lowerCamelCase__   =[]
						for i in range(len(__lowerCAmelCase							)							):
												new_matrix.append(top_left[i] + top_right[i]							)
						for i in range(len(__lowerCAmelCase							)							):
												new_matrix.append(bot_left[i] + bot_right[i]							)
						return new_matrix





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   list:




						'''simple docstring'''



						if matrix_dimensions(__lowerCAmelCase							)[1] != matrix_dimensions(__lowerCAmelCase							)[0]:
												lowerCamelCase__   =(
												    "Unable to multiply these matrices, please check the dimensions.\n"
												    F'''Matrix A: {matrixa}\n'''
												    F'''Matrix B: {matrixa}'''
												)
												raise Exception(__lowerCAmelCase							)
						lowerCamelCase__   =matrix_dimensions(__lowerCAmelCase							)
						lowerCamelCase__   =matrix_dimensions(__lowerCAmelCase							)

						if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
												return [matrixa, matrixa]

						lowerCamelCase__   =max(*__lowerCAmelCase  ,       *__lowerCAmelCase							)
						lowerCamelCase__   =int(math.pow(2  ,       math.ceil(math.loga(__lowerCAmelCase							)							)							)							)
						lowerCamelCase__   =matrixa
						lowerCamelCase__   =matrixa

						# Adding zeros to the matrices so that the arrays dimensions are the same and also
						# power of 2
						for i in range(0  ,       __lowerCAmelCase							):
												if i < dimensiona[0]:
																		for _ in range(dimensiona[1]  ,       __lowerCAmelCase							):
																								new_matrixa[i].append(0							)
												else:
																		new_matrixa.append([0] * maxim							)
												if i < dimensiona[0]:
																		for _ in range(dimensiona[1]  ,       __lowerCAmelCase							):
																								new_matrixa[i].append(0							)
												else:
																		new_matrixa.append([0] * maxim							)

						lowerCamelCase__   =actual_strassen(__lowerCAmelCase  ,       __lowerCAmelCase							)

						# Removing the additional zeros
						for i in range(0  ,       __lowerCAmelCase							):
												if i < dimensiona[0]:
																		for _ in range(dimensiona[1]  ,       __lowerCAmelCase							):
																								final_matrix[i].pop()
												else:
																		final_matrix.pop()
						return final_matrix


if __name__ == "__main__":
	a				=[
	    [2, 3, 4, 5],
	    [6, 4, 3, 1],
	    [2, 3, 6, 7],
	    [3, 1, 2, 4],
	    [2, 3, 4, 5],
	    [6, 4, 3, 1],
	    [2, 3, 6, 7],
	    [3, 1, 2, 4],
	    [2, 3, 4, 5],
	    [6, 2, 3, 1],
	]
	a				=[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
	print(strassen(matrixa, matrixa))


